The actual meaning of negative number can be regarded as a mirror, and negative number is the image in the mirror.
A growth rate of -0.07 means negative population growth, that is, the population growth of this country is 7% less than that of the previous year.
The elevator went up to the second floor, which means the elevator went down to the second floor.
The practical significance of imaginary numbers Most people are familiar with two kinds of numbers, namely, positive numbers (+5,
+17.5) and negative number (-5,-17.5). Negative numbers are medieval.
Ji is used to deal with problems such as 3-5. From the ancient point of view, this is necessary.
It seems impossible to subtract five apples from three apples. However, in the middle ages,
Businessmen have obviously realized the concept of default. "Please give me five apples.
Sure, but I only have three apples, so I still owe you two apples. "
This is equivalent to saying: (+3)-(+5) = (-2).
Positive numbers and negative numbers can be multiplied by each other according to some strict rules. Positive multiplication
Positive number, whose product is positive. Multiply a positive number by a negative number, and the product is negative. Most importantly,
When a negative number is multiplied by a negative number, the product is positive.
Therefore, (+1) × (+1) = (+1);
(+ 1)×(- 1)=(- 1);
(- 1)×(- 1)=(+ 1)。
Now suppose we ask ourselves: What number squared will produce+1? Or use
What is the square root of+1 in mathematical language?
There are two answers to this question. One answer is+1, because (+1)
×(+ 1)=(+ 1); Another answer is-1, because (-1).
×(- 1)=(+ 1)。 Mathematicians use √ (+ 1) = 1.
Represents this answer. (Note by Bi Sheng: (+1) under the root sign)
Now let's ask this question further: the square root of-1 is
How much/how much?
We feel a little embarrassed about this question. The answer is not+1, because
The square of+1 is+1; The answer is not-1 because the power of-1 is the same.
The sample is+1. Of course, (+1) × (-1) = (-1), but this is
Multiplication of two different numbers, not multiplication of one number.
In this way, we can create a number and give it a special symbol.
For example, # 1, and give it the following definition: # 1 is squared and you get it.
-1, that is, (#1) × (#1) = (-1). When this idea
When it was first put forward, mathematicians called this number "imaginary number" just because.
This number does not exist in the digital system they are used to. In fact, this first
Integrals are no more illusory than ordinary "real numbers". This so-called "imaginary number" has
Some strictly defined attributes, like general real numbers, are easy to handle.
However, it is precisely because mathematicians think that this number is somewhat imaginary that it is given.
This number has a special symbol "I" (imaginary number). We can put the positive
The imaginary number is written as (+I), the negative imaginary number is written as (-I), and+1 is regarded as.
Is a positive real number,-1 is regarded as a negative real number. So we can
Say √ ~ (-1) = i.
The real number system can completely correspond to the imaginary number system. Just like +5,
-17.32, +3/ 10 and other real numbers, we can also have them.
+5i,-17.32i, +3i/ 10 and other imaginary numbers.
We can even draw an imaginary system when drawing.
If a positive real number is represented by a straight line with zero as the midpoint.
Then, this system is a positive real number on one side of zero and a positive real number on the other side of zero.
Is a negative real number.
In this way, when you pass the zero point, make a straight line that intersects the straight line at right angles.
Then you can represent the imaginary system along the second straight line. The second straight line
The number on the zero side of a straight line is a positive imaginary number, and the number on the other side of the zero is a negative imaginary number.
In this way, using these two digital systems at the same time, you can put
All the figures are shown. For example, (+2)+(+3i) or
(+3)+(-2i). These numbers are "complex numbers".
Mathematicians and physicists have found that all points on a plane are the same number.
It is very useful that word systems are interrelated. If there is no imaginary number, he
Children will not be able to do this.
What is the practical meaning of complex numbers? 1 and I define the whole complex system (complex plane), which makes the theory of complex coefficient algebraic equation reach a perfect self-consistent system, that is, the basic theorem of algebra: any n-degree complex coefficient algebraic equation has only n roots in the complex field (multiple roots are counted).
The actual meaning of the opposite number is 1. North and east are positive, and south and west are negative, as can be seen from the coordinate axis.
2. Balance sheet. If the income is positive, the expenditure is negative.
3. Statement of assets and equity. If the assets are positive, the equity is negative.
4. Table loan. If the debit is positive, the credit is negative.
5. Represents creditor's rights and debts, with creditor's rights being positive and debts being negative.
Positive and negative, such as big and small, more and less, just like I am older than you 1 year, and you are one year younger than me.
Average: It reflects the average size of a group of data, and is usually used to represent the overall "average level" of data.
What is the practical significance of the operational research examination number? The number of tests in the simplex method is actually the difference between the market price of the product (variable) and the implied cost of the product. If the market price is higher than the implied cost, that is, the number of inspections is greater than zero, the product can be put into production, otherwise it will not be produced.
What is the practical significance of learning linear algebra? Linear algebra is a way of thinking to deal with linear problems. Now it has been widely used in engineering technology. I really didn't feel anything when I first saw these definitions and theorems. But they did play a very important role. Give some answers to the questions. The following answer may be somewhat theoretical.
The first contact should be "ranking". One of the most important characteristics of vector group, matrix and linear mapping. It is introduced by the maximal linearly independent group of vector groups, which reflects the linear correlation degree of vector groups and is extended to matrices and even linear mappings. The typical application of matrix rank is to discuss the number of basic solution systems of linear equations and solve the solution structure of linear equations. The solution of linear equations is still very important even now, because computers can only solve problems "linearly", so all problems must be linearized before computer processing.
In fact, rank has many applications (statistics, numerical calculation). N-dimensional vector space is abstracted from our real space. It's hard to say its application. In fact, many concepts in mathematics are basic, and a perfect theory is based on these concepts. The latter has good applications, but the former is difficult to involve these applications, but it is useless if it is not applied.
As for matrix multiplication, it was originally developed from linear equations. In fact, all the operations are given by us. This includes four operations. Matrix operation is produced by the application of (linear equations), and more importantly, it has many good properties, which makes it very easy to deal with problems. In essence, from the perspective of space, matrix multiplication makes the matrix become a mapping from space Rn to Rm space. As for adjoint matrix, it is also the product of the study of linear equations, but later we found that adjoint matrix can completely describe the inverse matrix of reversible matrix. Finally, I want to say that not all concepts have their practical applications. However, these seemingly useless concepts and theorems pave the way for truly widely used concepts and theorems.
What is an imaginary number? What is the practical significance of imaginary numbers? The concept of imaginary number
The unit I of imaginary number was first deduced by Euler. He takes the prefix of imaginary number as the unit of imaginary number, I = √- 1, so all imaginary numbers have the form of bi. Real numbers correspond to imaginary numbers, including rational numbers and irrational numbers, that is, real numbers.
Imaginary number, people began to call it "the ghost of real number", Descartes called it "imaginary number" in 1637, so all imaginary numbers have BI, while complex numbers have a=bi, where A and B are real numbers. Imaginary numbers are also often called pure imaginary numbers.
Since cardano's Da Yan Shu, imaginary numbers have been shrouded in mystery for 200 years. By 1797, wessel gave the image representation of the dotted line, and the reasonable position of the imaginary number was established. Together with Algan, he gave the geometric explanation of complex numbers with the help of the plane coordinate system established by Descartes, a French mathematician in the17th century, which is recognized by the mathematical community. Later, Gauss established a one-to-one correspondence between points and complex numbers on the rectangular coordinate plane, and imaginary numbers were widely known.